(e) the height of one square pyramid is 12 m. a similar pyramid has a height of 6 m. the volume of the larger pyramid is 400 m3. determine each of the following, showing all your work and reasoning. (a) scale factor of the smaller pyramid to the larger pyramid in simplest form (f) ratio of the areas of the bases of the smaller pyramid to the larger pyramid (g) ratio of the volume of the smaller pyramid to the larger (h) volume of the smaller pyramid

Step-by-step explanation:

Height (h₁) of one square pyramid = 12 m

A similar pyramid has a height h₂ = 6 m

(a)  Therefore scale factor of smaller pyramid to the larger pyramid = = =  1 : 2

(f)   Since ratio of the sides of smaller to larger pyramid is 1 : 2

so ratio of area of the bases = =

=

(g)  Ratio of volume of smaller to larger pyramid

= =

(h)  Since = and V₁ = 400 m³

So   =  ⇒ =

V₂ = = 50 m³

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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